Subgradient-Based Markov Chain Monte Carlo Particle Methods for Discrete-Time Nonlinear Filtering

This work shows how a carefully designed instrumental distribution can improve the performance of a Markov chain Monte Carlo (MCMC) filter for systems with a high state dimension. We propose a special subgradient-based kernel from which candidate moves are drawn. This facilitates the implementation of the filtering algorithm in high dimensional settings using a remarkably small number of particles. We demonstrate our approach in solving a nonlinear non-Gaussian high-dimensional problem in comparison with a recently developed block particle filter and over a dynamic compressed sensing (l1 constrained) algorithm. The results show high estimation accuracy

Scalable learning with a structural recurrent neural network for short-term traffic prediction

This paper presents a scalable deep learning approach for short-term traffic prediction based on historical traffic data in a vehicular road network. Capturing the spatio-temporal relationship of the big data often requires a significant amount of computational burden or an ad-hoc design aiming for a specific type of road network. To tackle the problem, we combine a road network graph with recurrent neural networks (RNNs) to construct a structural RNN (SRNN). The SRNN employs a spatio-temporal graph to infer the interaction between adjacent road segments as well as the temporal dynamics of the time series data. The model is scalable thanks to two key aspects. First, the proposed SRNN architecture is built by using the semantic similarity of the spatio-temporal dynamic interactions of all segments. Second, we design the architecture to deal with fixed-length tensors regardless of the graph topology. With the real traffic speed data measured in the city of Santander, we demonstrate the proposed SRNN outperforms the image-based approaches using the capsule network (CapsNet) by 14.1% and the convolutional neural network (CNN) by 5.87%, respectively, in terms of root mean squared error (RMSE). Moreover, we show that the proposed model is scalable. The SRNN model trained with data of a road network is able to predict traffic data of different road networks, with the fixed number of parameters to train

Structural recurrent neural network for traffic speed prediction

Deep neural networks have recently demonstrated the traffic prediction capability with the time series data obtained by sensors mounted on road segments. However, capturing spatio-temporal features of the traffic data often requires a significant number of parameters to train, increasing compu- tational burden. In this work we demonstrate that embedding topological information of the road network improves the process of learning traffic features. We use a graph of a ve- hicular road network with recurrent neural networks (RNNs) to infer the interaction between adjacent road segments as well as the temporal dynamics. The topology of the road network is converted into a spatio-temporal graph to form a structural RNN (SRNN). The proposed approach is validated over traffic speed data from the road network of the city of Santander in Spain. The experiment shows that the graph- based method outperforms the state-of-the-art methods based on spatio-temporal images, requiring much fewer parameters to trai

Robust Rauch-Tung-Striebel smoothing framework for heavy-tailed and/or skew noises

A novel robust Rauch-Tung-Striebel smoothing framework is proposed based on a generalized Gaussian scale mixture (GGScM) distribution for a linear state-space model with heavy-tailed and/or skew noises. The state trajectory, mixing parameters and unknown distribution parameters are jointly inferred using the variational Bayesian approach. As such, a major contribution of this work is unifying results within the GGScM distribution framework. Simulation and experimental results demonstrate that the proposed smoother has better accuracy than existing smoothers

A novel progressive Gaussian approximate filter with variable step size based on a variational Bayesian approach

The selection of step sizes in the progressive Gaussian ap- proximate filter (PGAF) is important, and it is difficult to se- lect optimal values in practical applications. Furthermore, in the PGAF, significant integral approximation errors are gener- ated by the repeated approximate calculations of the Gaussian weighted integrals, which results in an inaccurate measure- ment noise covariance matrix (MNCM). To solve these prob- lems, in this paper, the step sizes and the MNCM are jointly estimated based on the variational Bayesian (VB) approach. By incorporating the adaptive estimates of step sizes and the MNCM into the PGAF framework, a novel PGAF with vari- able step size is proposed. Simulation results illustrate that the proposed filter has higher estimation accuracy than exist- ing state-of-the-art nonlinear Gaussian approximate filters

A capsule network for traffic speed prediction in complex road networks

This paper proposes a deep learning approach for traffic flow prediction in complex road networks. Traffic flow data from induction loop sensors are essentially a time series, which is also spatially related to traffic in different road segments. The spatio-temporal traffic data can be converted into an image where the traffic data are expressed in a 3D space with respect to space and time axes. Although convolutional neural networks (CNNs) have been showing surprising performance in understanding images, they have a major drawback. In the max pooling operation, CNNs are losing important information by locally taking the highest activation values. The inter-relationship in traffic data measured by sparsely located sensors in different time intervals should not be neglected in order to obtain accurate predictions. Thus, we propose a neural network with capsules that replaces max pooling by dynamic routing. This is the first approach that employs the capsule network on a time series forecasting problem, to our best knowledge. Moreover, an experiment on real traffic speed data measured in the Santander city of Spain demonstrates the proposed method outperforms the state-of-the-art method based on a CNN by 13.1% in terms of root mean squared error

A Novel Robust Rauch-Tung-Striebel Smoother Based on Slash and Generalized Hyperbolic Skew Student’s T-Distributions

In this paper, a novel robust Rauch-Tung-Striebel smoother is proposed based on the Slash and generalized hyperbolic skew Student’s t-distributions. A novel hierarchical Gaussian state-space model is constructed by formulating the Slash distribution as a Gaussian scale mixture form and formulating the generalized hyperbolic skew Student’s t-distribution as a Gaussian variance-mean mixture form, based on which the state trajectory, mixing parameters and unknown noise parameters are jointly inferred using the variational Bayesian approach. The posterior probability density functions of mixing parameters of the Slash and generalized hyperbolic skew Student’s t-distributions are, respectively, approximated as truncated Gamma and generalized inverse Gaussian. Simulation results illustrate that the proposed robust Rauch-Tung-Striebel smoother has better estimation accuracy than existing state-of-the-art smoothers

Gaussian processes for RSS fingerprints construction in indoor localization

Location-based applications attract more and more attention in recent years. Examples of such applications include commercial advertisements, social networking software and patient monitoring. The received signal strength (RSS) based location fingerprinting is one of the most popular solutions for indoor localization. However, there is a big challenge in collecting and maintaining a relatively large RSS fingerprint database. In this work, we propose and compare two algorithms namely, the Gaussian process (GP) and Gaussian process with variogram, to estimate and construct the RSS fingerprints with incomplete data. The fingerprint of unknown reference points is estimated based on measurements at a limited number of surrounding locations. To validate the effectiveness of both algorithms, experiments using Bluetooth-low-energy (BLE) infrastructure have been conducted. The constructed RSS fingerprints are compared to the true measurements, and the result is analyzed. Finally, using the constructed fingerprints, the localization performance of a probabilistic fingerprinting method is evaluated

Outlier-robust Schmidt-Kalman filter using variational inference

The Schmidt-Kalman filter (SKF) achieves filtering consistency in the presence of biases in system dynamic and measurement models through accounting for their impacts when updating the state estimate and covariance. However, the performance of the SKF may break down when the measurements are subject to non-Gaussian and heavy-tail noise. To address this, we impose the Wishart prior distribution on the precision matrix of measurement noise, such that the measurement likelihood now has heavier tails than the Gaussian distribution to deal with the potential occurrence of outliers. Variational inference is invoked to establish analytically tractable methods for computing the posterior of the system state, system biases, and the measurement noise precision matrix. The principle of the SKF considers the effect of system biases but does not actively estimate them when two variants of outlier-robust SKFs are incorporated. We evaluate their performance in terms of estimation accuracy and filtering consistency using simulations and real-world data. Promising results are obtained

Computer vision methods for automating high temperature steel section sizing in thermal images

This paper proposes a solution to autonomously measuring steel sections with images captured by a monocular, uncalibrated thermal camera. A fast structural random forest algorithm extracts the edges of the steel sections from sequentially coming image data. Two approaches are proposed that recognize the edges and remotely evaluate the size of the manufacturing objects of interest, which will facilitate automating the steel manufacturing process. Four sets of experiments are conducted, and the results show that our method achieves accurate dimension measuring results, with a root mean square error less than 2:5 mm, which is the maximum tolerance bound of the manufacturing process